This thesis examines extracellular afterpotentials in the retina of Drosophila melanogaster. The results presented, and comparison of these with the available intracellular recordings, indicate that the ERG of Drosophila is a scaled down version of the transmembrane potentials of classes of retinula cells. The afterpotentials investigated are due to retinula cells R1-R6. Afterpotentials in photoreceptors are known to be associated with bi-stable visual pigments. Evidence is presented which suggests that the prolonged depolarising afterpotential (PDA) of R1-R6 in Drosophila results from a component of the membrane conductance of those cells which is correlated with the quantity of metarhodopsin (M580) generated by a stimulus. A simulation, using a membrane model and assuming the M580-conductance, predicts a number of the experimental findings: for example, a high negative correlation between the ERG d.c. potential and the size of the ERG response to a testflash, and a aignoidal decline of the d.c. potential when M580 is eliminated by longwave-length light. The simulation also predicts effects upon the classic V-log I curve which are detected in the Calliphora data of Razmjoo and Hamdorf (1976). Some of the phenomena of the FDA reported in other species (Limulus polyphemus) can only be replicated in Drosophila after small doses of blue light which induce "brief afterpotentials". These phenomena (decay of the afterpotential independently of the decay of metarhodopsin and suppression of the afterpotential by previoss metarhodopsin to rhodopsin conversion) have been taken by others as evidence for an "excitor-inhibitor" model of phototransduction. The value of this model is questioned and a biophysical model of the events in the Drosophila photoreceptors is presented. The afterpotential is shown to occur in wildtype (red eyed) Drosophila, and to have behavioural consequences. A model of extracellular potentials based on capacitance is advanced. This may shed light on electrical potentials in entracellular compartments such as the retina of insects.